Part (a)
Place yourself at point X. Face directly north. Then rotate clockwise 240° until you are facing point Y. The remaining 360-240 = 120 degrees is the measure of 'a'
Answer: a = 120°
===========================================================
Part (b)
Law of Cosines
(YZ)^2 = (XY)^2 + (XZ)^2 - 2*XY*XZ*cos(X)
(YZ)^2 = (20)^2 + (18)^2 - 2*20*18*cos(120)
(YZ)^2 = 1084
YZ = sqrt(1084)
YZ = 32.924155
YZ = 33
Answer: 33 km
===========================================================
Part (c)
Law of Sines
sin(Z)/XY = sin(X)/YZ
sin(Z)/20 = sin(120)/32.924155
sin(Z) = 20*sin(120)/32.924155
sin(Z) = 0.526073
Z = arcsin(0.526073) or Z = 180-arcsin(0.526073)
Z = 31.740505 or Z = 148.259495
Z = 32 or Z = 148
The angle Z = 148 is not possible since a triangle can't have more than one obtuse angle.
Answer: 32°